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ICSE Class 10 Answered

x^3+12x/6x^2+8= y^3+27y/9y^2+27 .using componendo find x:y
Asked by omkumbharjune | 09 Jun, 2019, 10:45: AM
answered-by-expert Expert Answer
begin mathsize 16px style fraction numerator straight x cubed plus 12 straight x over denominator 6 straight x squared plus 8 end fraction equals fraction numerator straight y cubed plus 27 straight y over denominator 9 straight y squared plus 27 end fraction end style
By componendo-dividendo,
begin mathsize 16px style fraction numerator begin display style straight x cubed plus 12 straight x plus 6 straight x squared plus 8 end style over denominator begin display style straight x cubed plus 12 straight x minus 6 straight x squared minus 8 end style end fraction equals fraction numerator begin display style straight y cubed plus 27 straight y plus 9 straight y squared plus 27 end style over denominator begin display style straight y cubed plus 27 straight y minus 9 straight y squared minus 27 end style end fraction end style
begin mathsize 16px style open parentheses straight x plus 2 close parentheses cubed over open parentheses straight x minus 2 close parentheses cubed equals fraction numerator begin display style open parentheses straight y plus 3 close parentheses cubed end style over denominator begin display style open parentheses straight y minus 3 close parentheses cubed end style end fraction end style
begin mathsize 16px style fraction numerator straight x plus 2 over denominator straight x minus 2 end fraction equals fraction numerator straight y plus 3 over denominator straight y minus 3 end fraction end style
By componendo-dividendo,
begin mathsize 16px style fraction numerator straight x plus 2 plus straight x minus 2 over denominator straight x plus 2 minus straight x plus 2 end fraction equals fraction numerator straight y plus 3 plus straight y minus 3 over denominator straight y plus 3 minus straight y plus 3 end fraction end style
begin mathsize 16px style fraction numerator 2 straight x over denominator 4 end fraction equals fraction numerator 2 straight y over denominator 6 end fraction end style
begin mathsize 16px style straight x over 2 equals straight y over 3 end style
begin mathsize 16px style straight x over straight y equals 2 over 3 end style

Answered by Sneha shidid | 10 Jun, 2019, 09:35: AM

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